Improved asynchronous stabilization method for nonhomogeneous Markovian jump fuzzy systems with incomplete transition rates

Abstract

This paper proposes an improved asynchronous stabilization method for nonhomogeneous Markovian jump fuzzy systems (MJFSs) with incomplete transition rates via a nonparallel distributed compensation (non-PDC) control scheme. To cover a more realistic situation in the continuous-time MJFS domain, this paper focuses on addressing the following issues differently from previous studies: 1) emergence of a nonhomogeneous Markov process and asynchronous control mode, 2) separation of the Lyapunov matrix from the control gain within stabilization conditions, and 3) relaxation of stabilization conditions subject to multiple time-varying parameters. Specifically, the effects of nonhomogeneity and asynchronism are simultaneously reflected in the stabilization conditions, and separation and relaxation techniques are additionally developed as needed. Finally, the advantages of our method are illustrated through two examples: the first is provided to show the effectiveness of the proposed separation technique, and the second is provided to show that the relaxed stabilization conditions are less conservative than previous results.